Counting balanced ternary designs (Q2713612)

The paper concerns balanced incomplete block designs on \(v\) elements with blocks of size 3, where each pair of distinct elements is in two blocks. Furthermore, each element occurs singly in \(\rho _1\) blocks and doubly in \(\rho _2\) blocks. Every possible 3-block configuration corresponds to one of 65 templates, and the paper contains formulae that express the occurence number for each of these templates in terms of \(v,\rho _1,\rho _2\) and in terms of further nine variables (these correspond to certain 2-block and 3-block configurations that are regarded as basic). A balanced ternary design with \(\rho _2 = 0\) is a balanced incomplete block design, and formulae for such designs need just two variables.